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https://doi.org/10.1140/epjc/s10052-019-6779-3

Regular Article - Theoretical Physics

## Ultra-relativistic gravity has properties associated with the strong force

^{1}
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK

^{2}
Viterbi School of Engineering, University of Southern California, Los Angeles, CA, 90089-2560, USA

^{*} e-mail: tf227@cam.ac.uk

Received:
10
August
2018

Accepted:
12
March
2019

Published online:
23
March
2019

The equations of motion, as well as the potential energy *V* of a self-gravitating *N*-body system in the first post-Minkowskian approximation have recently been derived. Here, for the particular case of two equal masses, the ultra-relativistic limit of these equations is analysed. It is shown that the requirement that the component of the gravitational force along the vector connecting the two particles is attractive, implies that the ultra-relativistic gravitational force acting on these two particles has properties usually associated with the strong force, namely, confinement and asymptotic freedom. This surprising result may have implications in particle physics: if the typical length of the system is of the order of the size of the pion, and if the mass of each particle is of the order of the mass of a light quark, then the magnitude of the above force is of the order of the magnitude of the strong force, whereas the bound state of this two equal masses body system yields a particle of mass of the order of the mass of the pion.

*© The Author(s), 2019*